Problem All square roots are periodic when written as continued fractions and can be written in the form: For example, let us consider ?23: If we continue we would get the following expansion: The process can be summarised as follows: It can be seen that the sequence is repeating. For conciseness, we use the notation [...]

Problem It is well known that if the square root of a natural number is not an integer, then it is irrational. The decimal expansion of such square roots is infinite without any repeating pattern at all. The square root of two is 1.41421356237309504880…, and the digital sum of the first one hundred decimal digits [...]

Problem Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae: The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three interesting properties. The set is cyclic, in that the last two digits of each number is the first two digits of the [...]

Bit Syntax in Erlang One of the often under-appreciated features of Erlang is its Bit Syntax for parsing and pattern matching binary data at a bit level. For instance, to pare TCP segments you can write something along the line of: The same capability can be applied to anything binary protocols, such as video encoding, [...]

I love this part of the year, there are great conferences happening between now and Feb, and I’m honoured to have been accepted as speaker to some of these amazing events.   Functional Finance (London) Oct 31st I’ll be giving a talk on taming complex APIs with F#-powered DSLs, using a number of popular AWS [...]